Various biological factors help maintain genome organization, but the genome’s own inherent polymeric structure and connectivity provide the foundation for its complex and dynamic architecture. We probe the extent to which the connectivity of the underlying polymer structure maintains chromatin organization through analysis of Hi-C genome contact maps and polymer molecular dynamics simulations. We cut the chromatin structure into ~10 kb fragments by treating nuclei with restriction enzymes and generate contact maps of the resulting structures via Hi-C after different time delays. We observe loss of compartmentalization and alterations to the contact probability scaling across multiple length scales after time delays of minutes to hours. To explain these observations, we construct a block copolymer simulation model for chromatin, which forms spatially distinct compartments via phase separation under normal conditions. Upon progressive fragmentation of the polymer, compartmentalization is progressively lost and other physical properties of the model genome are perturbed. The model illustrates how the underlying connectivity of chromatin along with other biophysical factors act together to maintain spatial organization of the genome.